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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Ground-based infrared spectroscopic measurements of atmospheric hydrogen cyanide

A number of lines of the nu-3 band of hydrogen cyanide have been detected in solar absorption spectra recorded near sunrise and sunset at Kitt Peak National Observatory (elevation 2095 m) with a 0.01/cm resolution Fourier transform spectrometer. Analysis of two of the strongest and best isolated lines has led to a value of 2.73 x 10 to the 15th molecules/sq cm for the vertical column abundance of HCN above Kitt Peak. The accuracy of this value is estimated as + or - 25%. This result, combined with the stratospheric concentration of HCN derived by Coffey, Mankin, and Cicerone (1981), yields 166 parts per trillion by volume for the average mixing ratio of HCN between 2 and 12 km. This is the first determination of the HCN concentration in the nonurban troposphere.

Rinsland, C. P.↗
NASA NTRS1983

Carbon monoxide mixing ratio inference from gas filter radiometer data

A new algorithm has been developed which permits, for the first time, real time data reduction of nadir measurements taken with a gas filter correlation radiometer to determine tropospheric carbon monoxide concentrations. The algorithm significantly reduces the complexity of the equations to be solved while providing accuracy comparable to line-by-line calculations. The method is based on a regression analysis technique using a truncated power series representation of the primary instrument output signals to infer directly a weighted average of trace gas concentration. The results produced by a microcomputer-based implementation of this technique are compared with those produced by the more rigorous line-by-line methods. This algorithm has been used in the reduction of Measurement of Air Pollution from Satellites, Shuttle, and aircraft data.

Wallio, H. A.↗
NASA NTRS1990

A numerical method for prediction of compressible turbulent flows with closure models

A new computer code to solve the time averaged Navier-Stokes equations is developed. Many of the state-of-the-art numerical techniques and algorithms have been tested and implemented in the program in order to achieve a better numerical accuracy and code efficiency. Various turbulence models are tested for a wide range of flows. The initial focus has been on two-equation eddy-viscosity models, which are the most advanced available in current compressible flow codes. The long term goal will be to test Reynolds-Stress models and to explore their performance in the high Mach number range. Although testing and improvement of turbulence models for supersonic and hypersonic flows is the primary objective of this research, part of the effort has been devoted to analyzing the vortex breakdown phenomena using new computer programs. Some preliminary results on the breakdown of a vortex flow in a tube are reported. Present calculations are restricted to two dimensional flow geometry.

Huang, P. G.↗
DOE OSTI2025

Strategic Placement and Sizing of Distributed Generation for Resilience Enhancement of Distribution Grids With Microgrid Formation

The rise in frequency and severity of extreme weather events highlights the need for resilient power distribution networks. Microgrids can help improve the resilience of distribution grids by providing continuous power supply using local distribution generation (DG) when the distribution grid fails. In this paper, we propose an approach for optimal placement and sizing of DG to form multiple microgrids throughout the distribution network by restoration actions such as switching operations in case of distribution grid outages caused by extreme weather events. Considering the randomness of damaged distribution lines, the DG placement and sizing problem is formulated as a two-stage stochastic mixed-integer program, with the first stage determining the placement and size of DG, and the second stage focusing on minimizing the amount of load shedding through network restoration and microgrid formations for each scenario. Due to the large number of scenarios, the sample average approximation (SAA) method is employed to solve the problem. The results of case studies on a modified IEEE 33 bus distribution grid demonstrate the effectiveness of the proposed DG placement and sizing strategy in improving the resilience of distribution grids by allowing the formation of multiple microgrids. In addition, the robustness and accuracy of the SAA method are validated through various case studies.

Distributed generation planning↗
DOE OSTI2021

An overview of wind-energy-production prediction bias, losses, and uncertainties

Abstract. The financing of a wind farm directly relates to the preconstruction energy yield assessments which estimate the annual energy production for the farm. The accuracy and the precision of the preconstruction energy estimates can dictate the profitability of the wind project. Historically, the wind industry tended to overpredict the annual energy production of wind farms. Experts have been dedicated to eliminating such prediction errors in the past decade, and recently the reported average energy prediction bias is declining. Herein, we present a literature review of the energy yield assessment errors across the global wind energy industry. We identify a long-term trend of reduction in the overprediction bias, whereas the uncertainty associated with the prediction error is prominent. We also summarize the recent advancements of the wind resource assessment process that justify the bias reduction, including improvements in modeling and measurement techniques. Additionally, because the energy losses and uncertainties substantially influence the prediction error, we document and examine the estimated and observed loss and uncertainty values from the literature, according to the proposed framework in the International Electrotechnical Commission 61400-15 wind resource assessment standard. From our findings, we highlight opportunities for the industry to move forward, such as the validation and reduction of prediction uncertainty and the prevention of energy losses caused by wake effect and environmental events. Overall, this study provides a summary of how the wind energy industry has been quantifying and reducing prediction errors, energy losses, and production uncertainties. Finally, for this work to be as reproducible as possible, we include all of the data used in the analysis in appendices to the article.

17 WIND ENERGY↗
DOE OSTI2023

Deep learning for morphological identification of extended radio galaxies using weak labels

Abstract The present work discusses the use of a weakly-supervised deep learning algorithm that reduces the cost of labelling pixel-level masks for complex radio galaxies with multiple components. The algorithm is trained on weak class-level labels of radio galaxies to get class activation maps (CAMs). The CAMs are further refined using an inter-pixel relations network (IRNet) to get instance segmentation masks over radio galaxies and the positions of their infrared hosts. We use data from the Australian Square Kilometre Array Pathfinder (ASKAP) telescope, specifically the Evolutionary Map of the Universe (EMU) Pilot Survey, which covered a sky area of 270 square degrees with an RMS sensitivity of 25–35 $\mu$ Jy beam $^{-1}$ . We demonstrate that weakly-supervised deep learning algorithms can achieve high accuracy in predicting pixel-level information, including masks for the extended radio emission encapsulating all galaxy components and the positions of the infrared host galaxies. We evaluate the performance of our method using mean Average Precision (mAP) across multiple classes at a standard intersection over union (IoU) threshold of 0.5. We show that the model achieves a mAP $_{50}$ of 67.5% and 76.8% for radio masks and infrared host positions, respectively. The network architecture can be found at the following link: https://github.com/Nikhel1/Gal-CAM

Astronomy & Astrophysics↗
DOE OSTI2024

Ultraviolet H 2 luminescence in molecular clouds induced by cosmic rays

Context. Galactic cosmic rays (CRs) play a crucial role in ionisation, dissociation, and excitation processes within dense cloud regions where UV radiation is absorbed by dust grains and gas species. CRs regulate the abundance of ions and radicals, leading to the formation of more and more complex molecular species, and determine the charge distribution on dust grains. A quantitative analysis of these effects is essential for understanding the dynamical and chemical evolution of star-forming regions. Aims. The CR-induced photon flux has a significant impact on the evolution of the dense molecular medium in its gas and dust components. This study evaluates the flux of UV photons generated by CRs to calculate the photon-induced dissociation and ionisation rates of a vast number of atomic and molecular species, as well as the integrated UV photon flux. Methods. To achieve these goals, we took advantage of recent developments in the determination of the spectra of secondary electrons, in the calculation of state-resolved excitation cross sections of H 2 by electron impact, and of photodissociation and photoionisation cross sections. Results. We calculated the H 2 level population of each rovibrational level of the X, B, C, B′, D, B″, D′, and a states. We then computed the UV photon spectrum of H 2 in its line and continuum components between 72 and 700 nm, with unprecedented accuracy, as a function of the CR spectrum incident on a molecular cloud, the H 2 column density, the isomeric H 2 composition, and the dust properties. The resulting photodissociation and photoionisation rates are, on average, lower than previous determinations by a factor of about 2, with deviations of up to a factor of 5 for the photodissociation of species such as AlH, C 2 H 2 , C 2 H 3 , C 3 H 3 , LiH, N 2 , NaCl, NaH, O 2 + , S2, SiH, l-C 4 , and l-C 5 H. A special focus is given to the photoionisation rates of H 2 , HF, and N 2 , as well as to the photodissociation of H 2 , which we find to be orders of magnitude higher than previous estimates. We give parameterisations for both the photorates and the integrated UV photon flux as a function of the CR ionisation rate, which implicitly depends on the H 2 column density, as well as the dust properties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

"Spectrally gapped" random walks on networks: a Mean First Passage Time formula

We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only input the transition probabilities into the target node. It is derived from the calculation of the average resolvent of a deformed ensemble of random sub-stochastic matrices H=\langle H\rangle +\delta H H = ⟨ H ⟩ + δ H , with \langle H\rangle ⟨ H ⟩ rank- 1 1 and non-negative. The accuracy of the formula depends on the spectral gap of the reduced transition matrix, and it is tested numerically on several instances of (weighted) networks away from the high sparsity regime, with an excellent agreement.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Ultraviolet H 2 luminescence in molecular clouds induced by cosmic rays

Context. Galactic cosmic rays (CRs) play a crucial role in ionisation, dissociation, and excitation processes within dense cloud regions where UV radiation is absorbed by dust grains and gas species. CRs regulate the abundance of ions and radicals, leading to the formation of more and more complex molecular species, and determine the charge distribution on dust grains. A quantitative analysis of these effects is essential for understanding the dynamical and chemical evolution of star-forming regions. Aims. The CR-induced photon flux has a significant impact on the evolution of the dense molecular medium in its gas and dust components. This study evaluates the flux of UV photons generated by CRs to calculate the photon-induced dissociation and ionisation rates of a vast number of atomic and molecular species, as well as the integrated UV photon flux. Methods. To achieve these goals, we took advantage of recent developments in the determination of the spectra of secondary electrons, in the calculation of state-resolved excitation cross sections of H 2 by electron impact, and of photodissociation and photoionisation cross sections. Results. We calculated the H 2 level population of each rovibrational level of the X, B, C, B', D, B", D', and a states. We then computed the UV photon spectrum of H 2 in its line and continuum components between 72 and 700 nm, with unprecedented accuracy, as a function of the CR spectrum incident on a molecular cloud, the H 2 column density, the isomeric H 2 composition, and the dust properties. The resulting photodissociation and photoionisation rates are, on average, lower than previous determinations by a factor of about 2, with deviations of up to a factor of 5 for the photodissociation of species such as AlH, C 2 H 2 , C 2 H 3 , C 3 H 3 , LiH, N 2 , NaCl, NaH, O$^+_2$, S 2 , SiH, l-C 4 , and l-C 5 H. A special focus is given to the photoionisation rates of H 2 , HF, and N 2 , as well as to the photodissociation of H 2 , which we find to be orders of magnitude higher than previous estimates. We give parameterisations for both the photorates and the integrated UV photon flux as a function of the CR ionisation rate, which implicitly depends on the H 2 column density, as well as the dust properties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Spatial distributions of X CO 2 seasonal cycle amplitude and phase over northern high-latitude regions

Satellite-based observations of atmospheric carbon dioxide (CO 2 ) provide measurements in remote regions, such as the biologically sensitive but undersampled northern high latitudes, and are progressing toward true global data coverage. Recent improvements in satellite retrievals of total column-averaged dry air mole fractions of CO 2 (X CO 2 ) from the NASA Orbiting Carbon Observatory 2 (OCO-2) have allowed for unprecedented data coverage of northern high-latitude regions, while maintaining acceptable accuracy and consistency relative to ground-based observations, and finally providing sufficient data in spring and autumn for analysis of satellite-observed X CO 2 seasonal cycles across a majority of terrestrial northern high-latitude regions. Here, we present an analysis of X CO 2 seasonal cycles calculated from OCO-2 data for temperate, boreal, and tundra regions, subdivided into 5° latitude by 20° longitude zones. We quantify the seasonal cycle amplitudes (SCAs) and the annual half drawdown day (HDD). OCO-2 SCAs are in good agreement with ground-based observations at five high-latitude sites, and OCO-2 SCAs show very close agreement with SCAs calculated for model estimates of X CO 2 from the Copernicus Atmosphere Monitoring Services (CAMS) global inversion-optimized greenhouse gas flux model v19r1 and the CarbonTracker2019 model (CT2019B). Model estimates of X CO 2 from the GEOS-Chem CO 2 simulation version 12.7.2 with underlying biospheric fluxes from CarbonTracker2019 (GC-CT2019) yield SCAs of larger magnitude and spread over a larger range than those from CAMS, CT2019B, or OCO-2; however, GC-CT2019 SCAs still exhibit a very similar spatial distribution across northern high-latitude regions to that from CAMS, CT2019B, and OCO-2. Zones in the Asian boreal forest were found to have exceptionally large SCA and early HDD, and both OCO-2 data and model estimates yield a distinct longitudinal gradient of increasing SCA from west to east across the Eurasian continent. In northern high-latitude regions, spanning latitudes from 47 to 72° N, longitudinal gradients in both SCA and HDD are at least as pronounced as latitudinal gradients, suggesting a role for global atmospheric transport patterns in defining spatial distributions of X CO2 seasonality across these regions. GEOS-Chem surface contact tracers show that the largest X CO 2 SCAs occur in areas with the greatest contact with land surfaces, integrated over 15–30d. The correlation of X CO 2 SCA with these land surface contact tracers is stronger than the correlation of X CO 2 SCA with the SCA of CO 2 fluxes or the total annual CO 2 flux within each 5° latitude by 20° longitude zone. This indicates that accumulation of terrestrial CO 2 flux during atmospheric transport is a major driver of regional variations in X CO 2 SCA.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1977

The effects of participatory mode and task workload on the detection of dynamic system failures

The ability of operators to detect step changes in the dynamics of control systems is investigated as a joint function of, (1) participatory mode: whether subjects are actively controlling those dynamics or are monitoring an autopilot controlling them, and (2) concurrent task workload. A theoretical analysis of detection in the two modes identifies factors that will favor detection in either mode. Three subjects detected system failures in either an autopilot or manual controlling mode, under single-task conditions and concurrently with a subcritical tracking task. Latency and accuracy of detection were assessed and related through a speed accuracy tradeoff representation. It was concluded that failure detection performance was better during manual control than during autopilot control, and that the extent of this superiority was enhanced as dual-task load increased. Ensemble averaging and multiple regression techniques were then employed to investigate the cues utilized by the subjects in making their detection decisions.

Wickens, C. D.↗
NASA NTRS1991

Computational modelling of dump combustors flowfield

A computational model aimed at predicting the flowfield of dump combustors is presented. The turbulent combustion model is based on the conserved scalar approach and on a convenient specification of its probability density function, which reduces the computation of the mean density to a closed form. Turbulence is modeled by means of the k-epsilon model. The averaged conservation equations are solved by a technique based on a staggered grid and on the SIMPLE solver. The computational model is applied to a simple dump combustor to assess the computer time requirements and accuracy. The turbulent combustion model is shown to reduce the computer time by an order of magnitude when compared to evaluating the mean density by numerical quadrature.

Lentini, D.↗
NASA NTRS1993

Coherent lidar design and performance verification

The verification of LAWS beam alignment in space can be achieved by a measurement of heterodyne efficiency using the surface return. The crucial element is a direct detection signal that can be identified for each surface return. This should be satisfied for LAWS but will not be satisfied for descoped LAWS. The performance of algorithms for velocity estimation can be described with two basic parameters: the number of coherently detected photo-electrons per estimate and the number of independent signal samples per estimate. The average error of spectral domain velocity estimation algorithms are bounded by a new periodogram Cramer-Rao Bound. Comparison of the periodogram CRB with the exact CRB indicates a factor of two improvement in velocity accuracy is possible using non-spectral domain estimators. This improvement has been demonstrated with a maximum-likelihood estimator. The comparison of velocity estimation algorithms for 2 and 10 micron coherent lidar was performed by assuming all the system design parameters are fixed and the signal statistics are dominated by a 1 m/s rms wind fluctuation over the range gate. The beam alignment requirements for 2 micron are much more severe than for a 10 micron lidar. The effects of the random backscattered field on estimating the alignment error is a major problem for space based lidar operation, especially if the heterodyne efficiency cannot be estimated. For LAWS, the biggest science payoff would result from a short transmitted pulse, on the order of 0.5 microseconds instead of 3 microseconds. The numerically errors for simulation of laser propagation in the atmosphere have been determined as a joint project with the University of California, San Diego. Useful scaling laws were obtained for Kolmogorov atmospheric refractive turbulence and an atmospheric refractive turbulence characterized with an inner scale. This permits verification of the simulation procedure which is essential for the evaluation of the effects of refractive turbulence on coherent Doppler lidar systems. The analysis of 2 micron Doppler lidar data from Coherent Technologies, Inc. (CTI) has demonstrated many of the advantages of doppler lidar measurements of boundary layer winds. The effects of wind shear and wind turbulence over the pulse volume are probably the dominant source of the reduced performance. The effects of wind shear and wind turbulence on the statistical description of doppler lidar data has been derived and calculated.

Frehlich, Rod↗
DOE OSTI2023

A Method for Projecting Cloud Shadows Onto a Central Receiver Field to Predict Receiver Damage

This work demonstrates methods of mapping high-spatial-resolution direct normal irradiance (DNI) data from satellites, Total Sky Imagers (TSIs), and analogous data sources onto a heliostat field for characterizing the spatial and temporal variation of the incident flux on a central receiver tower during cloud transient events. The mapping methods are incorporated into an optical software module that interfaces with CoPylot–SolarPILOT’s python API– to provide computationally efficient optical simulation of the heliostat field and the solar power tower. Eventually, this optical model will be incorporated into optimization models whereby a plant operator can understand the effects of cloud transient events on overall power production and receiver lifetime due to creep-fatigue damage and therefore make better informed decisions about receiver shutdown events. By more accurately modelling the effects of cloud events on receiver flux maps, this work may determine the magnitude and frequency of thermal cycling on receiver tubes and panels using actual or realistic cloud shapes instead of averaged DNI values–which may undercount the total cycle number. This work may also prevent unnecessary plant shutdowns due to overly precautionary control strategies and characterize the relative impact of various cloud types on receiver life. We plan to eventually integrate this methodology into the System Advisor Model (SAM) to improve performance model accuracy during periods of cloudiness. In this paper, we demonstrate generating DNI maps and mapping them to a solar field in CoPylot using 10 m resolution data from publicly available Sentinel-2 satellite data over the Crescent Dunes plant.

Mullin, Matthew↗
DOE OSTI2024

RANSBox: A zero-dimensional modular software package for Reynolds-averaged Navier-Stokes modeling

RANSBox is a zero-dimensional software package for Reynolds-averaged Navier-Stokes (RANS) modeling developed at Lawrence Livermore National Laboratory to support common implementation of RANS models across a variety of host codes with different numerical schemes and code bases. Herein this work describes the key features of RANSBox including “model-agnostic integration,” which allows new models to be implemented in RANSBox and quickly deployed to host codes without additional changes to the host code base. Three one-dimensional test problems with analytical asymptotic properties are described which can be used to verify correctness of RANSBox integration. Results for these problems are then compared across different RANS models in a single code and across different codes with a common RANS model. By using a common model implementation in RANSBox, host codes with different numerical schemes and formal orders of accuracy are demonstrated to predict the expected behavior for the three test problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2011

Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration

A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and sets up initial conditions and integrates; (2) a routine that calculates system reduced derivatives using recurrence relations for quotients and products; and (3) a routine that determines the step size and sums the series. The order of accuracy used in a trajectory calculation is arbitrary and can be set by the user. The algorithm directly calculates the motion of other planetary bodies and does not require ephemeris files (except to start the calculation). The code also runs with Taylor series and Runge-Kutta used interchangeably for different phases of a mission.

Scott, James R.↗
DOE OSTI2022

Physics-guided machine learning for improved accuracy of the National Solar Radiation Database

The National Solar Radiation Database (NSRDB) provides high-resolution spatiotemporal solar irradiance data for the entire globe. The NSRDB uses a two-step Physical Solar Model (PSM) to compute the effects of clouds and other atmospheric variables on the solar radiation reaching the surface of the Earth. Physical and optical cloud properties are fundamental inputs to the PSM and are derived from the National Oceanic and Atmospheric Administration's Geostationary Operational Environmental Satellites. This paper describes recent improvements to the NSRDB driven by physics-guided machine learning methods for cloud property retrieval. The impacts of these new methods on the NSRDB irradiance data are validated using an extensive set of ground measurement sites, showing significant improvement for all sites. We report on average, the mean absolute percentage error for global horizontal irradiance and direct normal irradiance show reductions of 2.16 and 3.95 percentage points respectively for all daylight conditions, 5.92 and 17.39 percentage points respectively for cloudy conditions, and 9.00 and 22.59 percentage points respectively for gap-filled cloudy conditions. These new methods will help improve the quality and accuracy of the irradiance and cloud data in the NSRDB.

14 SOLAR ENERGY↗
DOE OSTI2023

Deep learning closure models for large-eddy simulation of flows around bluff bodies

Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.

Mechanics↗